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website/content/ChapterFour/0062.Unique-Paths.md

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+# [62. Unique Paths](https://leetcode.com/problems/unique-paths/)
+
+
+## 题目
+
+A robot is located at the top-left corner of a *m* x *n* grid (marked 'Start' in the diagram below).
+
+The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
+
+How many possible unique paths are there?
+
+![](https://assets.leetcode.com/uploads/2018/10/22/robot_maze.png)
+
+Above is a 7 x 3 grid. How many possible unique paths are there?
+
+**Note**: *m* and *n* will be at most 100.
+
+**Example 1**:
+
+    Input: m = 3, n = 2
+    Output: 3
+    Explanation:
+    From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
+    1. Right -> Right -> Down
+    2. Right -> Down -> Right
+    3. Down -> Right -> Right
+
+**Example 2**:
+
+    Input: m = 7, n = 3
+    Output: 28
+
+
+## 题目大意
+
+一个机器人位于一个 m x n 网格的左上角 （起始点在下图中标记为“Start” ）。机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角（在下图中标记为“Finish”）。问总共有多少条不同的路径？
+
+
+## 解题思路
+
+- 这是一道简单的 DP 题。输出地图上从左上角走到右下角的走法数。
+- 由于机器人只能向右走和向下走，所以地图的第一行和第一列的走法数都是 1，地图中任意一点的走法数是 `dp[i][j] = dp[i-1][j] + dp[i][j-1]`
+
+## 代码
+
+```go
+
+package leetcode
+
+func uniquePaths(m int, n int) int {
+	dp := make([][]int, n)
+	for i := 0; i < n; i++ {
+		dp[i] = make([]int, m)
+	}
+	for i := 0; i < m; i++ {
+		dp[0][i] = 1
+	}
+	for i := 0; i < n; i++ {
+		dp[i][0] = 1
+	}
+	for i := 1; i < n; i++ {
+		for j := 1; j < m; j++ {
+			dp[i][j] = dp[i-1][j] + dp[i][j-1]
+		}
+	}
+	return dp[n-1][m-1]
+}
+
+```